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On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids |
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| Authors: | Mohyuddin M R Hayat T Mahomed F M Asghar S Siddiqui A M |
| Institution: | (1) Department of Mathematics, Quaid-i-Azam University, 45320 Islamabad, Pakistan;(2) School of Computational & Applied Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits, 2050 Johannesburg, South Africa;(3) COMSATS, Institute of Information and Technology, Abbottabad, Pakistan;(4) Pennsylvania State University, York Campus, York, PA, 17403, U.S.A. |
| Abstract: | Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions. |
| Keywords: | axisymmetric cylindrical coordinates inverse methods non-linear equations second-grade fluid steady and unsteady flows swirling flows |
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